Question 1

$\frac{4 \mathrm{x}}{5 \mathrm{x}+35}+\frac{28}{5 \mathrm{x}+35}$

Accepted Answer

A)  $\frac{4}{5}$ 
B)  $\frac{2}{5}$ 
C)  $\frac{4 x+28}{2(5 x+35)}$ 
D)  $\frac{4 x+28}{5 x+35}$ 
A)  $\frac{4}{5}$ 
B)  $\frac{2}{5}$ 
C)  $\frac{4 x+28}{2(5 x+35)}$ 
D)  $\frac{4 x+28}{5 x+35}$ A

Question 2

Simplify the complex fraction.
-$\frac{\frac{8}{x}-\frac{x}{8}}{\frac{1}{8}-\frac{1}{x}}$

Accepted Answer

A)  $8 x(x+8)$ 
B)  $-(x+8)$ 
C)  $-(x-8)$ 
D)  $x+8$ 
A)  $8 x(x+8)$ 
B)  $-(x+8)$ 
C)  $-(x-8)$ 
D)  $x+8$ B

Question 3

$\frac{x^{2}-36}{x} \div \frac{5 x+30}{x-6}$

Accepted Answer

A)  $\frac{(x-6)^{2}}{x}$ 
B)  $\frac{5 x}{(x-6)^{2}}$ 
C)  $\frac{(x-6)^{2}}{5 x}$ 
D)  $\frac{5(x+6)^{2}}{x}$ 
A)  $\frac{(x-6)^{2}}{x}$ 
B)  $\frac{5 x}{(x-6)^{2}}$ 
C)  $\frac{(x-6)^{2}}{5 x}$ 
D)  $\frac{5(x+6)^{2}}{x}$ C

Question 4

For the given functions $f(x)$ and $g(x)$, find $f(x) \cdot g(x)$.
-$f(x)=\frac{x^{2}+5 x+6}{x^{2}+8 x+12}, g(x)=\frac{x^{2}-5 x-6}{x^{2}+4 x+3}$

Accepted Answer

A)  $\frac{x-6}{x+6}$ 
B)  -1 
C)  $\frac{x+6}{x-6}$ 
D)  1 
A)  $\frac{x-6}{x+6}$ 
B)  -1 
C)  $\frac{x+6}{x-6}$ 
D)  1

Question 5

Simplify the complex fraction.
-$\frac{\frac{x^{2}-81}{x^{2}+16 x+63}}{\frac{x^{2}+3 x-28}{x^{2}+2 x-35}}$

Accepted Answer

A)  $\frac{(x+7)(x-5)}{n(x)}$ 
B)  $\frac{(x+9)(x-5)}{2 x}$ 
C)  $\frac{(x-9)(x+5)}{(-9 x}$ 
D)  $\frac{(x-9)(x-5)}{2 n}$ 
A)  $\frac{(x+7)(x-5)}{n(x)}$ 
B)  $\frac{(x+9)(x-5)}{2 x}$ 
C)  $\frac{(x-9)(x+5)}{(-9 x}$ 
D)  $\frac{(x-9)(x-5)}{2 n}$

Question 6

Find the missing numerator and denominator.
-$\frac{x+4}{x-7} \cdot \frac{?}{?}=\frac{(x+4)(x-1)}{(x-7)(x+3)}$

Accepted Answer

A)  $\frac{x-1}{x+3}$ 
B)  $\frac{x(x-1)}{x(x+3)}$ 
C)  $\frac{x+1}{x-3}$ 
D)  $\frac{x(4 x-1)}{x(7 x+3)}$ 
A)  $\frac{x-1}{x+3}$ 
B)  $\frac{x(x-1)}{x(x+3)}$ 
C)  $\frac{x+1}{x-3}$ 
D)  $\frac{x(4 x-1)}{x(7 x+3)}$

Question 7

$\frac{x^{2}-8 x}{x-3}+\frac{15}{x-3}$

Accepted Answer

A)  $x-5$ 
B)  $x+5$ 
C)  $x-3$ 
D)  $\frac{x^{2}-8 x+15}{x-3}$ 
A)  $x-5$ 
B)  $x+5$ 
C)  $x-3$ 
D)  $\frac{x^{2}-8 x+15}{x-3}$

Question 8

Simplify the complex fraction.
-$\frac{2 x+\frac{4}{x}}{\frac{1}{3 x^{2}}+\frac{1}{6}}$

Accepted Answer

A)  $\frac{12 x\left(x^{2}+2\right)}{\left(x^{2}+1\right)}$ 
B)  $12 x$ 
C)  $\frac{12}{x}$ 
D)  $6 x$ 
A)  $\frac{12 x\left(x^{2}+2\right)}{\left(x^{2}+1\right)}$ 
B)  $12 x$ 
C)  $\frac{12}{x}$ 
D)  $6 x$

Question 9

One printer can do a printing job in 9 hours. Another printer can do the same job in 13 hours. How long can they do the job working together?

Accepted Answer

A)  $5 \frac{2}{23}$ hours 
B)  $5 \frac{7}{22}$ hours 
C)  $\frac{1}{22}$ hours 
D)  $29 \frac{1}{4}$ hours 
A)  $5 \frac{2}{23}$ hours 
B)  $5 \frac{7}{22}$ hours 
C)  $\frac{1}{22}$ hours 
D)  $29 \frac{1}{4}$ hours

Question 10

The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $220 \mathrm{~cm}^{3}$ under a pressure of $18 \mathrm{~kg} / \mathrm{cm}^{2}$. What will be its volume under a pressure of $30 \mathrm{~kg} / \mathrm{cm}^{2}$ ?

Accepted Answer

A)  $367 \mathrm{~cm}^{3}$ 
B)  $132 \mathrm{~cm}^{3}$ 
C)  $145 \mathrm{~cm}^{3}$ 
D)  $385 \mathrm{~cm}^{3}$ 
A)  $367 \mathrm{~cm}^{3}$ 
B)  $132 \mathrm{~cm}^{3}$ 
C)  $145 \mathrm{~cm}^{3}$ 
D)  $385 \mathrm{~cm}^{3}$

Question 11

$y$ varies directly as $x$. If $y=63$ when $x=9$, find $y$ when $x=3$.

Accepted Answer

A)  81 
B)  49 
C)  21 
D)  9 
A)  81 
B)  49 
C)  21 
D)  9

Question 12

Solve for the specified variable
-$I=\frac{n E}{n r+R}$ for $n$

Accepted Answer

A)  $n=\frac{I(n r+R)}{E}$ 
B)  $n=I R-E+I r$ 
C)  $n=\frac{I R}{I r-E}$ 
D)  $n=\frac{I R}{E-I r}$ 
A)  $n=\frac{I(n r+R)}{E}$ 
B)  $n=I R-E+I r$ 
C)  $n=\frac{I R}{I r-E}$ 
D)  $n=\frac{I R}{E-I r}$

Question 13

Find all values of the variable for which the rational expression is undefined.
-$\frac{x^{2}-16}{x^{2}-3 x-40}$

Accepted Answer

A)  $-8,5$ 
B)  0 
C)  $-4,4$ 
D)  $-5,8$ 
A)  $-8,5$ 
B)  0 
C)  $-4,4$ 
D)  $-5,8$

Question 14

$\frac{x}{x-9}+\frac{8}{x-9}$

Accepted Answer

A)  $\frac{x-8}{x-9}$ 
B)  $\frac{x+8}{x-9}$ 
C)  $\frac{x-8}{2(x-9)}$. 
D)  $\frac{x+8}{2(x-9)}$ 
A)  $\frac{x-8}{x-9}$ 
B)  $\frac{x+8}{x-9}$ 
C)  $\frac{x-8}{2(x-9)}$. 
D)  $\frac{x+8}{2(x-9)}$

Question 15

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$, and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$.
-$f(x)=\frac{1}{4 x-11}$

Accepted Answer

A)  $-\frac{2}{(4 x-11)^{2}}$ 
B)  $\frac{4}{(4 x-11)^{2}}$ 
C)  $\frac{2}{(4 x-11)^{2}}$ 
D)  $-\frac{4}{(4 x-11)^{2}}$ 
A)  $-\frac{2}{(4 x-11)^{2}}$ 
B)  $\frac{4}{(4 x-11)^{2}}$ 
C)  $\frac{2}{(4 x-11)^{2}}$ 
D)  $-\frac{4}{(4 x-11)^{2}}$

Question 16

Find the missing numerator and denominator.
-$\frac{6 x^{2}-18 x}{x^{2}-7 x-30} \div \frac{?}{?}=\frac{6 x}{x-10}$

Accepted Answer

A)  $\frac{x-10}{6 x}$ 
B)  $\frac{x-3}{x+3}$ 
C)  $\frac{6 x}{x+10}$ 
D)  $\frac{x+10}{6 x}$ 
A)  $\frac{x-10}{6 x}$ 
B)  $\frac{x-3}{x+3}$ 
C)  $\frac{6 x}{x+10}$ 
D)  $\frac{x+10}{6 x}$

Question 17

$\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}$

Accepted Answer

A)  $x+2$ 
B)  $\frac{x+2}{x}$ 
C)  $\frac{x+2}{x^{2}+7 x}$ 
D)  $\frac{x}{x^{2}+11 x+28}$ 
A)  $x+2$ 
B)  $\frac{x+2}{x}$ 
C)  $\frac{x+2}{x^{2}+7 x}$ 
D)  $\frac{x}{x^{2}+11 x+28}$

Question 18

The sum of a number and 6 times its reciprocal is 7. Find the number.

Accepted Answer

A)  6 
B)  1 
C)  1 or 6 
D)  7 
A)  6 
B)  1 
C)  1 or 6 
D)  7

Question 19

$\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}$

Accepted Answer

A)  $\frac{x-4}{x^{2}+6 x}$ 
B)  $x-4$ 
C)  $\frac{x}{x^{2}+12 x+36}$ 
D)  $\frac{x-4}{x}$ 
A)  $\frac{x-4}{x^{2}+6 x}$ 
B)  $x-4$ 
C)  $\frac{x}{x^{2}+12 x+36}$ 
D)  $\frac{x-4}{x}$

Question 20

Amy can clean the house in 7 hours. When she works together with Tom, the job takes 4 hours. How long would it take Tom, working by himself, to clean the house?

Accepted Answer

A)  $9 \frac{1}{3}$ hours 
B)  3 hours 
C)  $10 \frac{1}{3}$ hours 
D)  $9 \frac{2}{3}$ hours 
A)  $9 \frac{1}{3}$ hours 
B)  3 hours 
C)  $10 \frac{1}{3}$ hours 
D)  $9 \frac{2}{3}$ hours

$\frac{4 \mathrm{x}}{5 \mathrm{x}+35}+\frac{28}{5 \mathrm{x}+35}$

Simplify the complex fraction. - $\frac{\frac{8}{x}-\frac{x}{8}}{\frac{1}{8}-\frac{1}{x}}$

$\frac{x^{2}-36}{x} \div \frac{5 x+30}{x-6}$

For the given functions $f(x)$ and $g(x)$ , find $f(x) \cdot g(x)$ . - $f(x)=\frac{x^{2}+5 x+6}{x^{2}+8 x+12}, g(x)=\frac{x^{2}-5 x-6}{x^{2}+4 x+3}$

Simplify the complex fraction. - $\frac{\frac{x^{2}-81}{x^{2}+16 x+63}}{\frac{x^{2}+3 x-28}{x^{2}+2 x-35}}$

Find the missing numerator and denominator. - $\frac{x+4}{x-7} \cdot \frac{?}{?}=\frac{(x+4)(x-1)}{(x-7)(x+3)}$

$\frac{x^{2}-8 x}{x-3}+\frac{15}{x-3}$

Simplify the complex fraction. - $\frac{2 x+\frac{4}{x}}{\frac{1}{3 x^{2}}+\frac{1}{6}}$

One printer can do a printing job in 9 hours. Another printer can do the same job in 13 hours. How long can they do the job working together?

The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $220 \mathrm{~cm}^{3}$ under a pressure of $18 \mathrm{~kg} / \mathrm{cm}^{2}$ . What will be its volume under a pressure of $30 \mathrm{~kg} / \mathrm{cm}^{2}$ ?

$y$ varies directly as $x$ . If $y=63$ when $x=9$ , find $y$ when $x=3$ .

Solve for the specified variable - $I=\frac{n E}{n r+R}$ for $n$

Find all values of the variable for which the rational expression is undefined. - $\frac{x^{2}-16}{x^{2}-3 x-40}$

$\frac{x}{x-9}+\frac{8}{x-9}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\frac{1}{4 x-11}$

Find the missing numerator and denominator. - $\frac{6 x^{2}-18 x}{x^{2}-7 x-30} \div \frac{?}{?}=\frac{6 x}{x-10}$

$\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}$

The sum of a number and 6 times its reciprocal is 7. Find the number.

$\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}$

Amy can clean the house in 7 hours. When she works together with Tom, the job takes 4 hours. How long would it take Tom, working by himself, to clean the house?

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

Exam 6: Rational Expressions and Equations

4x5x+35+285x+35\frac{4 \mathrm{x}}{5 \mathrm{x}+35}+\frac{28}{5 \mathrm{x}+35}5x+354x​+5x+3528​

Simplify the complex fraction. - 8x−x818−1x\frac{\frac{8}{x}-\frac{x}{8}}{\frac{1}{8}-\frac{1}{x}}81​−x1​x8​−8x​​

x2−36x÷5x+30x−6\frac{x^{2}-36}{x} \div \frac{5 x+30}{x-6}xx2−36​÷x−65x+30​

For the given functions f(x)f(x)f(x) and g(x)g(x)g(x) , find f(x)⋅g(x)f(x) \cdot g(x)f(x)⋅g(x) . - f(x)=x2+5x+6x2+8x+12,g(x)=x2−5x−6x2+4x+3f(x)=\frac{x^{2}+5 x+6}{x^{2}+8 x+12}, g(x)=\frac{x^{2}-5 x-6}{x^{2}+4 x+3}f(x)=x2+8x+12x2+5x+6​,g(x)=x2+4x+3x2−5x−6​

Simplify the complex fraction. - x2−81x2+16x+63x2+3x−28x2+2x−35\frac{\frac{x^{2}-81}{x^{2}+16 x+63}}{\frac{x^{2}+3 x-28}{x^{2}+2 x-35}}x2+2x−35x2+3x−28​x2+16x+63x2−81​​

Find the missing numerator and denominator. - x+4x−7⋅??=(x+4)(x−1)(x−7)(x+3)\frac{x+4}{x-7} \cdot \frac{?}{?}=\frac{(x+4)(x-1)}{(x-7)(x+3)}x−7x+4​⋅??​=(x−7)(x+3)(x+4)(x−1)​

x2−8xx−3+15x−3\frac{x^{2}-8 x}{x-3}+\frac{15}{x-3}x−3x2−8x​+x−315​

Simplify the complex fraction. - 2x+4x13x2+16\frac{2 x+\frac{4}{x}}{\frac{1}{3 x^{2}}+\frac{1}{6}}3x21​+61​2x+x4​​

One printer can do a printing job in 9 hours. Another printer can do the same job in 13 hours. How long can they do the job working together?

The volume VVV of a gas varies inversely as the pressure PPP on it. The volume of a gas is 220 cm3220 \mathrm{~cm}^{3}220 cm3 under a pressure of 18 kg/cm218 \mathrm{~kg} / \mathrm{cm}^{2}18 kg/cm2 . What will be its volume under a pressure of 30 kg/cm230 \mathrm{~kg} / \mathrm{cm}^{2}30 kg/cm2 ?

yyy varies directly as xxx . If y=63y=63y=63 when x=9x=9x=9 , find yyy when x=3x=3x=3 .

Solve for the specified variable - I=nEnr+RI=\frac{n E}{n r+R}I=nr+RnE​ for nnn

Find all values of the variable for which the rational expression is undefined. - x2−16x2−3x−40\frac{x^{2}-16}{x^{2}-3 x-40}x2−3x−40x2−16​

xx−9+8x−9\frac{x}{x-9}+\frac{8}{x-9}x−9x​+x−98​

Simplify the difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ , and evaluate as hhh approaches 0 to find the rate of change of f(x)f(x)f(x) . - f(x)=14x−11f(x)=\frac{1}{4 x-11}f(x)=4x−111​

Find the missing numerator and denominator. - 6x2−18xx2−7x−30÷??=6xx−10\frac{6 x^{2}-18 x}{x^{2}-7 x-30} \div \frac{?}{?}=\frac{6 x}{x-10}x2−7x−306x2−18x​÷??​=x−106x​

x2+8x+16x2+11x+28÷x2+4xx2+9x+14\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}x2+11x+28x2+8x+16​÷x2+9x+14x2+4x​

The sum of a number and 6 times its reciprocal is 7. Find the number.

x2+11x+30x2+12x+36÷x2+5xx2+2x−24\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}x2+12x+36x2+11x+30​÷x2+2x−24x2+5x​

Amy can clean the house in 7 hours. When she works together with Tom, the job takes 4 hours. How long would it take Tom, working by himself, to clean the house?

Review of Real Numbers

Linear and Absolute Value Equations and Inequalities

Graphing Linear Equations

Systems of Equations

Exponents, Polynomials, and Factoring Polynomials

Radical Expressions and Equations

Quadratic Equations

Logarithmic and Exponential Functions

Conic Sections

Sequences, Series, and the Binomial Theorem

Filters

$\frac{4 \mathrm{x}}{5 \mathrm{x}+35}+\frac{28}{5 \mathrm{x}+35}$

Simplify the complex fraction. - $\frac{\frac{8}{x}-\frac{x}{8}}{\frac{1}{8}-\frac{1}{x}}$

$\frac{x^{2}-36}{x} \div \frac{5 x+30}{x-6}$

For the given functions $f(x)$ and $g(x)$ , find $f(x) \cdot g(x)$ . - $f(x)=\frac{x^{2}+5 x+6}{x^{2}+8 x+12}, g(x)=\frac{x^{2}-5 x-6}{x^{2}+4 x+3}$

Simplify the complex fraction. - $\frac{\frac{x^{2}-81}{x^{2}+16 x+63}}{\frac{x^{2}+3 x-28}{x^{2}+2 x-35}}$

Find the missing numerator and denominator. - $\frac{x+4}{x-7} \cdot \frac{?}{?}=\frac{(x+4)(x-1)}{(x-7)(x+3)}$

$\frac{x^{2}-8 x}{x-3}+\frac{15}{x-3}$

Simplify the complex fraction. - $\frac{2 x+\frac{4}{x}}{\frac{1}{3 x^{2}}+\frac{1}{6}}$

The volume $V$ of a gas varies inversely as the pressure $P$ on it. The volume of a gas is $220 \mathrm{~cm}^{3}$ under a pressure of $18 \mathrm{~kg} / \mathrm{cm}^{2}$ . What will be its volume under a pressure of $30 \mathrm{~kg} / \mathrm{cm}^{2}$ ?

$y$ varies directly as $x$ . If $y=63$ when $x=9$ , find $y$ when $x=3$ .

Solve for the specified variable - $I=\frac{n E}{n r+R}$ for $n$

Find all values of the variable for which the rational expression is undefined. - $\frac{x^{2}-16}{x^{2}-3 x-40}$

$\frac{x}{x-9}+\frac{8}{x-9}$

Simplify the difference quotient $\frac{f(x+h)-f(x)}{h}$ , and evaluate as $h$ approaches 0 to find the rate of change of $f(x)$ . - $f(x)=\frac{1}{4 x-11}$

Find the missing numerator and denominator. - $\frac{6 x^{2}-18 x}{x^{2}-7 x-30} \div \frac{?}{?}=\frac{6 x}{x-10}$

$\frac{x^{2}+8 x+16}{x^{2}+11 x+28} \div \frac{x^{2}+4 x}{x^{2}+9 x+14}$

$\frac{x^{2}+11 x+30}{x^{2}+12 x+36} \div \frac{x^{2}+5 x}{x^{2}+2 x-24}$